CN104259005A - High-frequency and high-voltage power supply controller for electrostatic dust collection and control method - Google Patents

Abstract

The invention discloses a high-frequency high-voltage power supply controller and a control method for electrostatic dust removal, including a voltage conditioning circuit, a sliding mode controller, a fuzzy controller, a digital logic unit, and a driving circuit; a voltage transformer of the main circuit of the high-frequency high-voltage power supply The collected voltage is input to the voltage conditioning circuit. After conditioning, it is input into the sliding mode controller and the fuzzy controller. The fuzzy controller adjusts the sliding mode surface parameters of the sliding mode controller, and the output signal of the sliding mode controller passes through the digital logic unit. The PWM signal driving the switch is obtained, and the PWM signal drives the inverter circuit of the main circuit of the high-frequency high-voltage power supply through the driving circuit. The present invention applies the fuzzy sliding mode control to the high-frequency and high-voltage power supply for electrostatic dust removal, utilizes the sliding mode control to have strong robustness to system parameter changes and external disturbances, and improves the system performance when the reference voltage changes and load disturbances stability.

Description

High-frequency high-voltage power supply controller and control method for electrostatic dust removal

technical field

The invention relates to a high-frequency and high-voltage power supply for electrostatic dust removal, in particular to a controller and a control method for the high-frequency and high-voltage power supply, and belongs to the technical field of environmental protection equipment.

Background technique

With the rapid development of domestic industry, environmental problems have followed. In recent years, air pollution has particularly hurt people's nerves. Days of haze weather has sounded the alarm for us. The formulation of new atmospheric emission standards has brought new challenges to the dust removal industry. requirements and opportunities. The more and more extensive application of high-frequency and high-voltage electrostatic precipitator power supplies in the dust removal industry also requires higher and higher performance requirements.

At present, the control method of domestic high-voltage electrostatic precipitator is mainly traditional PID control. In actual use, it is found that because the power control system is a lagging system, and the working environment is complex, with characteristics such as nonlinearity, variability and complexity, it is difficult to obtain an accurate mathematical model. It makes the traditional PID controller face the problem that the control parameters are difficult to select. Sliding mode control based on variable structure system theory shows insensitivity and robustness to system parameter changes and load disturbances, while fuzzy control can not only soften the control signal and reduce or avoid the jitter phenomenon of general sliding mode signals, fuzzy control It also has the ability of self-adaptation and self-learning, and can well realize the tuning of the parameters of the sliding surface. Therefore, it is very necessary to use fuzzy sliding mode controller to control the high frequency and high voltage power supply.

Contents of the invention

The object of the present invention is to provide a high-frequency and high-voltage power supply controller and control method for electrostatic dust removal, which can control the nonlinear loop of the high-frequency and high-voltage electrostatic dust removal power supply to realize zero-voltage shutdown (ZVS) of full-range loads, with fast dynamic Response, good tracking of the output voltage, so that the high-frequency power supply can adapt to various working conditions, especially in the case of sudden load changes, the output voltage transition time is short, the overshoot is small, and it has good robustness.

The purpose of the present invention is achieved through the following technical solutions:

A high-frequency and high-voltage power supply controller for electrostatic dust removal, including a voltage conditioning circuit 1, a sliding mode controller 2, a fuzzy controller 3, a digital logic unit 4, and a drive circuit 5, the sliding mode controller 2 and the fuzzy controller 3 Constitute a fuzzy sliding mode controller; the voltage collected by the voltage transformer of the main circuit of the high-frequency high-voltage power supply is input to the voltage conditioning circuit 1, and after conditioning, it is input into the sliding mode controller 2 and the fuzzy controller 3, and the fuzzy controller 3 controls the sliding mode The parameters of the sliding mode surface of the controller 2 are set and adjusted, the output signal of the sliding mode controller 2 passes through the digital logic unit 4 to obtain the PWM signal for driving the switch, and the PWM signal passes through the driving circuit 5 to drive the inverter circuit of the main circuit of the high frequency and high voltage power supply.

The object of the present invention can also be further realized by the following technical measures:

The aforementioned high-frequency and high-voltage power supply controller for electrostatic dust removal, in which the sliding mode controller 2 is constructed according to the sliding mode surface, firstly, according to the detected and adjusted power supply output voltage u ₀ , output reference voltage u _ref and voltage u _cp across the resonant capacitor, construct Sliding mode surface, the constructed sliding mode surface is:

$\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&Integral;</span><span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; ref</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; dt</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; cp</span>}}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}$

Where k _c , k _d are differential coefficients, k _p is proportional coefficients, k _i is integral coefficients, according to the arrival condition get control condition $u=\left\{\begin{array}{cc}0,& \mathrm{the\; s}<0\\ 1,& \mathrm{the\; s}>0\end{array}\right.,$ and Respectively, the average value of the output voltage u ₀ and the voltage u _cp at both ends of the resonant capacitor;

The sliding mode controller 2 includes an addition and subtraction link, an addition link, a first low-pass filter link, a second low-pass filter link, an absolute value link, an integral link, a differential link, a proportional differential link, a comparator, a clock and a trigger device; the subtraction input of the addition and subtraction link is the reference voltage u _ref of the output voltage of the power supply, the input terminal of the first low-pass filtering link is the output voltage u _o of the power supply, and the output voltage u _{o of} the power supply is filtered by the first low-pass filter The signal filtered by the link is input to the positive input terminal of the proportional differential link and the addition and subtraction link respectively, and the signal after the differential operation of the proportional differential link is input to the addition link; the power output voltage u _o passes through the first low-pass filter link The signal of the addition and subtraction of the input addition and subtraction link and the reference voltage u _ref is input to the addition link after passing through the integral link; the input of the absolute value link is the voltage u _cp across the capacitor of the resonant network, and the voltage u across the capacitor After _cp is filtered by the second low-pass filter link and differentiated by the differential link, it is input into the addition link; the output signal of the addition link is the sliding mode output signal, and the sliding mode output signal is an analog signal, and the sliding mode output signal is compared A set of digital signals is obtained by comparing with the zero potential at the trigger, and the digital signal and the clock signal are input into the flip-flop, and the flip-flop outputs a set of digital signals with high and low levels.

The aforementioned high-frequency and high-voltage power supply controller for electrostatic dust removal, wherein the fuzzy controller 3 adjusts the sliding mode surface parameters of the sliding mode controller 2 as follows:

The selected input language variables of fuzzy control are the difference e between the given output voltage u _ref and the actual output voltage u _o and the output voltage deviation change rate e _c , and the sliding mode surface parameters σk _p , σk _i , σk _d and σk _c are taken as output Language variables, according to the positive deviation and negative deviation of the output voltage detection value and the actual value of the output voltage, the size of the deviation e and deviation rate e _c is divided into {negative large, negative medium, negative small, zero, positive small, positive medium, positive large} 7 fuzzy subsets, denoted as {NB, NM, NS, ZO, PS, PM, PB}, respectively quantify the deviation e and deviation rate e _c into the area of (-3, 3), and the fuzzy controller The fuzzy subsets of output σk _p , σk _i , σk _d and σk _c are divided into {negative large, negative medium, negative small, zero, positive small, positive medium, positive large} seven fuzzy subsets, denoted as {NB, NM , NS, ZO, PS, PM, PB}, which are respectively quantized to (-0.25, 0.25), (-0.06, 0.06), (-3, 3), (-1, 1); input quantities e and e The membership function of _c is Gaussian, and the output membership functions are all triangular. The sliding mode surface parameter tuning algorithm is as follows:

k _p =k _p ′+σk _p , _ki = _ki ′+σk _i , k _d =k _d ′+σk _d , k _c =k _c ′+σk _c

Among them, k _p ′, _ki ′, k _d ′, and k _c ′ are the parameters of the sliding surface before tuning.

The aforementioned high-frequency and high-voltage power supply controller for electrostatic dust removal, wherein the fuzzy rule used by the fuzzy controller 3 to adjust the sliding mode surface parameters of the sliding mode controller 2 is:

If e is A and e _c is B;

THEN σk _p is C, σk _i is D, σk _d is E, σk _c is F.

The aforementioned high-frequency high-voltage power supply controller for electrostatic dust removal, wherein the fuzzy controller 3 is based on DSP.

Compared with the prior art, the beneficial effect of the present invention is: the present invention applies the fuzzy sliding mode control with good dynamic characteristic effect to the high-frequency high-voltage power supply for electrostatic dust removal, and utilizes the sliding mode control to effectively control system parameter changes and external disturbances. The feature of strong robustness improves the system stability when the reference voltage changes and the load is disturbed. The adaptive self-learning ability of fuzzy control is used to reduce or eliminate the jitter problem of sliding mode control and realize better sliding mode control. The invention improves the dynamic response speed of the system, has good adaptability to nonlinear loads, and makes the power supply suitable for various working conditions.

Description of drawings

Figure 1 is the overall structure diagram of the high-frequency and high-voltage power supply system for electrostatic dust removal;

Figure 2 is a block diagram of the sliding mode controller design process;

Fig. 3 (A) is the LCC resonant network equivalent circuit, and Fig. 3 (B) is the low-pass filter equivalent circuit;

Fig. 4 is a structural schematic diagram of a sliding mode controller;

Fig. 5 is a block diagram of fuzzy sliding mode control flow.

Detailed ways

The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

As shown in Figure 1, the power system includes two main circuits and a control circuit, in which the main circuit consists of a three-phase bridge rectifier 6, a full-bridge inverter circuit 7, an LCC resonant network 8, a high-frequency transformer 9, a high-voltage rectifier circuit 10 and The dust collector equivalent network is composed of 11. After the three-phase mains input is rectified by the three-phase bridge circuit 6, the inverter is realized in the full-bridge inverter circuit 7. After the inverter output, it passes through the LCC resonant network, boosts the voltage at the high-frequency transformer 9, and finally passes through the high-voltage rectification. The circuit 10 rectifies the output to the dust collector. The control loop is composed of a voltage conditioning circuit 1 , a sliding mode variable structure controller 2 , a fuzzy controller 3 , a digital logic unit 4 , and a driving circuit 5 . The process of the main circuit part is as follows: the three-phase power supply is input into the three-phase bridge rectifier circuit, after rectification, it is input into the full-bridge inverter circuit for inversion, after passing through the resonant network, it is boosted by a high-frequency transformer, and the output of the transformer passes through a high-voltage rectifier circuit, and then loaded after rectification Work with the duster on. The control loop flow is as follows: the voltage collected by the voltage transformer is input into the voltage conditioning circuit 1, and after conditioning, it is input into the sliding mode variable structure controller 2 and the fuzzy controller 3, and the fuzzy controller 3 adjusts the parameters of the sliding mode controller 2, The sliding mode controller 2 outputs a PWM signal for driving the switch through the digital logic unit 4 , and the signal drives the inverter circuit through the driving circuit 5 .

Design the fuzzy sliding mode controller in conjunction with the design process in Figure 2.

S1: Establish the state space model of the system. First, analyze the LCC resonant network shown in Figure 1 to obtain its equivalent circuit as shown in Figure 3. The load effect of the equivalent network of the dust collector on the resonant network in Figure 1 can be used A DC power supply _if to represent. The rectification network can be represented by a switch s. When u _cp >0, s is equivalent to being connected to position 1, and when u _cp <0, s is equivalent to being connected to position 2. The resonant network input is the output of the switching network, which can be represented by a voltage source u _ab . Figure 2 shows the equivalent circuit of the resonant network and the equivalent circuit of the low-pass filter. According to the equivalent circuit shown in Figure 2, the state space model of the system can be obtained:

$\left\{\begin{array}{c}\frac{{\mathrm{<span\; class="notranslate">\; di</span>}}_{\mathrm{<span\; class="notranslate">\; ls</span>}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; ab</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; cs</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; cp</span>}}<span\; class="notranslate">\; )</span>\\ \frac{{\mathrm{<span\; class="notranslate">\; du</span>}}_{\mathrm{<span\; class="notranslate">\; cs</span>}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; ls</span>}}}{{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}\\ \frac{{\mathrm{<span\; class="notranslate">\; du</span>}}_{\mathrm{<span\; class="notranslate">\; cp</span>}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}}<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; ls</span>}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}}{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; sgn</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; cp</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>\\ \frac{{\mathrm{<span\; class="notranslate">\; di</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}}<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; (</span>\frac{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; cp</span>}}<span\; class="notranslate">\; |</span>}{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}<span\; class="notranslate">\; )</span>\\ \frac{{\mathrm{<span\; class="notranslate">\; du</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}}<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}}{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}}<span\; class="notranslate">\; )</span>\end{array}\right.$

Among them, i _Ls , u _cs , u _cp are the resonant state variables which are inductor current, series capacitor voltage and parallel capacitor voltage respectively. if _f , u ₀ are the output state variables of the dust collector, that is, the inductor current and the output voltage of the power supply. The control input u is a discrete variable. When u = 1, it is the power-on mode, and when u = 0, it is the power-off mode.

S2: Establish the average large signal dynamic model of the system, based on the approximate sinusoidal characteristics of the resonant state variables i _Ls , u _cs , u _cp , assuming that the above state variables are pure sinusoidal signals with time-varying amplitude and phase, the expression is: $\left\{\begin{array}{c}{i}_{\mathrm{ls}}=I_{\mathrm{ls}}\&CenterDot;\sin {\mathrm{\&omega;}}_{0}t\\ u_{\mathrm{cs}}=V_{\mathrm{cs}}\&CenterDot;\sin ({\mathrm{\&omega;}}_{0}t-\mathrm{\&alpha;})\\ u_{\mathrm{cp}}=V_{\mathrm{cp}}\&CenterDot;\sin ({\mathrm{\&omega;}}_{0}t-\mathrm{\&beta;})\end{array}\right.,$ Among them, α and β are the phase difference between the voltage u _cs and the voltage u _cp respectively, and V _cs and V _cp are the peak values of the voltage, and they are variables that change slowly with time t. ω ₀ is the resonant frequency. Considering that the time scale of the output filter is much larger than that of the resonant network, and ignoring the ripple of the filter state variable, then _if , u ₀ can use a relatively accurate approximation Indicates that the same can be used and to represent the mean values of i _Ls and u _cs respectively, and can represent the mean values of α and β, respectively. The above mean value can be obtained by first substituting the approximate sinusoidal signal into the state space mathematical model of the system, replacing these elements with the fundamental wave components of nonlinear elements, and then balancing the coefficients of the linear combination of _sinωr t and _cosωr t by harmonics. The average large signal dynamic model is thus obtained as follows:

$\left\{\begin{array}{c}\frac{\mathrm{<span\; class="notranslate">\; d</span>}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; ls</span>}}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 4</span>}}{{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; ab</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; cs</span>}}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; cos</span>}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; cp</span>}}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; cos</span>}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}<span\; class="notranslate">\; )</span>\\ \frac{\mathrm{<span\; class="notranslate">\; d</span>}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; cs</span>}}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}<span\; class="notranslate">\; \&Center\; Dot;</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; ls</span>}}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; cos</span>}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}\\ \frac{\mathrm{<span\; class="notranslate">\; d</span>}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; cp</span>}}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}}<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; ls</span>}}}<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; cos</span>}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}<span\; class="notranslate">\; -</span>\frac{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}}}{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\frac{\mathrm{<span\; class="notranslate">\; 8</span>}}{{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; )</span>\\ \frac{\mathrm{<span\; class="notranslate">\; d</span>}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}}<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; (</span>\frac{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; cp</span>}}}}{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}}<span\; class="notranslate">\; )</span>\\ \frac{\mathrm{<span\; class="notranslate">\; d</span>}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}}<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}}<span\; class="notranslate">\; \&Center\; Dot;</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}}<span\; class="notranslate">\; )</span>\\ \frac{\mathrm{<span\; class="notranslate">\; d</span>}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>\frac{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; ls</span>}}}}{{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; Cs</span>}}}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; sin</span>}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}\\ \frac{\mathrm{<span\; class="notranslate">\; d</span>}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>\frac{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; ls</span>}}}}{{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; Cp</span>}}}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; sin</span>}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}\end{array}\right.$

S3: Select an appropriate sliding mode surface and design the sliding mode surface. First, calculate the relative coefficient of the output voltage u _0. It can be easily obtained that the highest order of the output voltage is 4, and the dynamic expression of the open-loop voltage can be obtained as:

${\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\frac{{\mathrm{<span\; class="notranslate">\; d</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}}{{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\frac{{\mathrm{<span\; class="notranslate">\; d</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}}{{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\frac{{\mathrm{<span\; class="notranslate">\; d</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}}{{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\frac{{\mathrm{<span\; class="notranslate">\; d</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; cp</span>}}}}{{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>$

Wherein, a ₄ =n·C ₀ ·L _f ·C _eq ; a ₃ =n·C _eq ·L _f a ₂ =n·C _eq ; a ₁ =C _eq ;

In order to find a suitable sliding surface, the output voltage is forced here to follow a fourth-order linear dynamic response. Thus the ideal closed-loop dynamic output voltage can be obtained:

${\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\frac{{\mathrm{<span\; class="notranslate">\; d</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}}{{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\frac{{\mathrm{<span\; class="notranslate">\; d</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}}{{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\frac{{\mathrm{<span\; class="notranslate">\; d</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}}{{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; ref</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}$

In the sliding model due to the invariant condition The existence of makes the converter dynamics move near the sliding surface s. Based on this feature, the ideal dynamic sliding mode surface can be found. The expression of the invariance condition can be obtained by making the difference between the above two formulas:

$\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Center\; Dot;</span>\frac{{\mathrm{<span\; class="notranslate">\; d</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}}{{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Center\; Dot;</span>\frac{{\mathrm{<span\; class="notranslate">\; d</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}}{{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Center\; Dot;</span>\frac{{\mathrm{<span\; class="notranslate">\; d</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}}{{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; ref</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\frac{{\mathrm{<span\; class="notranslate">\; d</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}}{{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}$

Select the appropriate sliding factor as follows

b ₄ =a ₄

b ₃ =a ₃

b ₁ =a ₁ +k _p

b ₀ =k _i

a ₁ =k _c

b ₂ =a ₂ +k _d

The expression of the sliding mode surface s can be obtained by integrating the invariant expression:

$\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&Integral;</span><span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; ref</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; dt</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; cp</span>}}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}$

final use condition get control condition $u=\left\{\begin{array}{cc}0,& \mathrm{the\; s}<0\\ 1,& \mathrm{the\; s}>0\end{array}\right..$

Use fuzzy control to adjust the parameters of the above sliding mode surface, select the input language variables as the difference e between the given output voltage u _ref and the actual output voltage u _o and the output voltage deviation change rate e _c , and take the parameters of the sliding mode surface σk _p , σk _i , σk _d and σk _c are the output language variables. The parameter tuning of the sliding mode surface is to find out the output voltage deviation e and the output voltage deviation change rate e _c and the sliding mode surface parameters σk _p , σk _i , σk _d and σk _c According to the fuzzy relationship among fuzzy control principles, the above four parameters are modified. According to the deviation between the output voltage detection value and the actual output voltage value (including positive deviation and negative deviation), the size of e and e _c is divided into {negative large, negative medium, negative small, zero, positive small, positive medium, positive large} 7 The fuzzy subset, denoted as {NB, NM, NS, ZO, PS, PM, PB}, respectively quantizes the deviation e and deviation rate e _c into the area of (-3, 3), and at the same time the output of the fuzzy controller The fuzzy subsets of σk _p , σk _i , σk _d and σk _c are divided into {negative large, negative medium, negative small, zero, positive small, positive medium, positive large} seven fuzzy subsets, which are denoted as {NB, NM, NS , ZO, PS, PM, PB}, which are quantized to (-0.25, 0.25), (-0.06, 0.06), (-3, 3), (-1, 1), respectively. The membership functions of the input quantities e and e _c are Gaussian, and the output membership functions are all triangular. The sliding mode surface parameter tuning algorithm is as follows:

k _p ＝k _p ′+σk _p

k _i =k _i ′+σk _i

k _d ＝k _d ′+σk _d

k _c =k _c +σk _c

During the online operation, the control system completes the setting of the parameters of the sliding surface by processing the results of the fuzzy logic rules, looking up tables and computing. The fuzzy rules used are:

If e is A and e _c is B

THEN σk _p is C, σk _i is D, σk _d is E, σk _c is F

S4: Design the fuzzy sliding mode controller. The sliding mode surface designed in step S3 can design the corresponding controller. As shown in Figure 4, the sliding mode controller includes addition and subtraction, addition, low-pass filtering, absolute Value elements, integral elements, differential elements, comparators, clocks, and flip-flops. The subtraction input of the addition and subtraction link is the reference voltage u _ref of the output voltage of the power supply, and the input terminal of the low-pass filter link is the output voltage u _o of the power supply. The signal filtered by the low-pass filter link is respectively input to the proportional integral differential link and The positive input terminal of the adder-subtractor is input into the addition link after the differential operation of the proportional differential link. After u _o passes through the low-pass filter link, it inputs the signal of addition and subtraction link and the reference voltage for addition and subtraction operation, and after passing the integration link, it enters the adder. The input of the absolute value link is the voltage u _cp at both ends of the capacitor of the resonant network, which is then filtered by the low-pass filter link and differentiated by the differential link, and then input to the addition link. The output signal of the addition link is the sliding mode output signal. The sliding mode output signal is an analog signal, and the signal is compared with the zero potential at the comparator to obtain a set of digital signals, the digital signal and the clock signal are input to the flip-flop, and the flip-flop outputs a set of frequency switching signals for high-low level conversion . The switching signal is logically processed in the digital logic unit to generate four pulse signals, and the pulse signal is generated by the driving circuit to supply the driving signal to the inverter circuit.

On the basis of the sliding mode controller in Figure 4, the sliding mode surface is adjusted according to the tuning method mentioned in step S3, the output of the fuzzy control and the parameters corresponding to the sliding mode surface are accumulated, and the sliding mode is realized through fuzzy control Surface adjustment. The combination of the two is the fuzzy sliding mode controller.

S5: Verify the stability of the fuzzy sliding mode controller. The closed-loop ideal dynamic characteristics of the system can be obtained by an equivalent control method. The ideal sliding dynamic model can be obtained by replacing the theoretical variable in the open-loop model with a new state variable:

$\left\{\begin{array}{c}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; Leq</span>}}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}}{{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&CenterDot;</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}}{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}}<span\; class="notranslate">\; )</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; ref</span>}}<span\; class="notranslate">\; )</span>\\ \frac{\mathrm{<span\; class="notranslate">\; d</span>}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; cp</span>}}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; eq</span>}}}<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; Leq</span>}}}<span\; class="notranslate">\; -</span>\frac{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}}}{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; )</span>\\ \frac{\mathrm{<span\; class="notranslate">\; d</span>}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}}<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; (</span>\frac{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; cp</span>}}}}{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}}<span\; class="notranslate">\; )</span>\\ \frac{\mathrm{<span\; class="notranslate">\; d</span>}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}}<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}}<span\; class="notranslate">\; -</span>\frac{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}}}{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}}<span\; class="notranslate">\; )</span>\\ \frac{\mathrm{<span\; class="notranslate">\; d</span>}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; cs</span>}}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 8</span>}}{{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; \&CenterDot;</span>\frac{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; Leq</span>}}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; cos</span>}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}}{{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; cos</span>}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}}\\ \frac{\mathrm{<span\; class="notranslate">\; d</span>}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 8</span>}}{{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; \&CenterDot;</span>\frac{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; Leq</span>}}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; sin</span>}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}}{{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; cs</span>}}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; cos</span>}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}}\\ \frac{\mathrm{<span\; class="notranslate">\; d</span>}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>\frac{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; Leq</span>}}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; the\; tan</span>}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}}{{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; eq</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; cp</span>}}}\end{array}\right.$

in From the dynamic model, we can find that the dynamic model is composed of two subsystems, the first four formulas constitute a linear subsystem, and the latter three formulas constitute a nonlinear subsystem, and these two subsystems are relatively independent and uncoupled. Therefore, the stability analysis can be carried out separately for these two systems. Applying linear techniques to linear systems we can use the following parameter ranges to ensure the stability of the system.

k _d >C ₀

$\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; <</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; <</span>\frac{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}}{\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; no</span>}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; eq</span>}}<span\; class="notranslate">\; )</span>$

$\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; <</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; <</span>\frac{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; R</span>}}{{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; eq</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}}<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; eq</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>$

The nonlinear subsystem represents the internal dynamic stability of the system. Using the zero dynamic analysis method, the internal dynamic stability has been verified by small-signal linearization. From this we can find that the internal system is stable and independent of the control parameters, so no additional conditions are required.

As shown in Fig. 5, the flow chart of the fuzzy sliding mode, after the collected output voltage u _o is A/D converted, the difference between the output and the reference voltage u _ref of the output voltage is made, and the sliding mode is constructed together with the voltage u _cp at both ends of the parallel capacitor The fuzzy controller adjusts the parameters of the sliding mode surface, and compares the output of the sliding mode surface with the zero potential to generate a control signal. The control signal forms a discrete control signal u after passing through the trigger unit. If the output of the sliding mode surface is lower than zero Potential then u=0, if it is higher than zero potential then u=1. The discrete control signal and the resonant current signal are input into the digital logic unit together, and the digital logic unit generates a trigger pulse signal after logical operation. This signal drives the dust removal power supply to work through the drive unit.

In addition to the above-mentioned embodiments, the present invention can also have other implementations, and all technical solutions formed by equivalent replacement or equivalent transformation fall within the scope of protection required by the present invention.

Claims (5)

1. an electrostatic precipitation high-frequency high-voltage source controller, it is characterized in that, comprise voltage modulate circuit (1), sliding mode controller (2), fuzzy controller (3), digital logic unit (4), drive circuit (5), described sliding mode controller (2), fuzzy controller (3) form Fuzzy Sliding Model Controller; The voltage input voltage modulate circuit (1) of the voltage transformer collection of high-frequency and high-voltage power supply main circuit, sliding mode controller (2) and fuzzy controller (3) is inputted after conditioning, the sliding-mode surface parameter of fuzzy controller (3) to sliding mode controller (2) is adjusted adjustment, the output signal of sliding mode controller (2) obtains the pwm signal of driving switch through digital logic unit (4), pwm signal drives the inverter circuit of high-frequency and high-voltage power supply main circuit through overdrive circuit (5).

2. electrostatic precipitation high-frequency high-voltage source controller as claimed in claim 1, is characterized in that, described sliding mode controller (2) builds according to sliding-mode surface, first good according to examine and debug electric power output voltage u ₀, output reference voltage u _refwith resonant capacitance both end voltage u _cp, build sliding-mode surface, constructed sliding-mode surface is:

$S=k_d\&CenterDot;\frac{d\stackrel{\&OverBar;}{u_0}}{\mathrm{dt}}+k_p\&CenterDot;\stackrel{\&OverBar;}{u_0}+k_i\&CenterDot;\&Integral;\left(\stackrel{\&OverBar;}{u_0}{-u}_{\mathrm{ref}}\right)\mathrm{dt}+k_c\&CenterDot;\frac{d\stackrel{\&OverBar;}{u_{\mathrm{cp}}}}{\mathrm{dt}}$

Wherein k _c, k _ddifferential coefficient, k _pproportionality coefficient, k _iintegral coefficient, according to reaching condition obtain controlled condition $u=\left\{\begin{array}{cc}0,& s<0\\ 1,& s>0\end{array}\right.,$ with be respectively output voltage u ₀with resonant capacitance both end voltage u _cpaverage;

Described sliding mode controller (2) comprises addition and subtraction link, addition link, the first LPF link, the second LPF link, absolute value link, integral element, differentiation element, proportion differential link, comparator, clock and trigger; The subtraction input of described addition and subtraction link is the reference voltage u of electric power output voltage _ref, the input of described first LPF link is electric power output voltage u _o, electric power output voltage u _obe input to the positive input terminal of proportion differential link and addition and subtraction link respectively through the filtered signal of the first LPF link, the signal after described proportion differential link is differentiated is input to addition link; Electric power output voltage u _oaddition and subtraction link and reference voltage u is inputted after the first LPF link _refcarry out the signal of plus and minus calculation, after integral element, input addition link; The electric capacity both end voltage u being input as resonant network of described absolute value link _cp, described electric capacity both end voltage u _cpaddition link is inputted after carrying out differential respectively through the second LPF link filtering and differentiation element; The output signal of described addition link is sliding formwork output signal, this sliding formwork output signal is analog signal, sliding formwork output signal is compared at comparator place and zero potential and obtains set of number signal, this data signal and clock signal input trigger, trigger exports the data signal of one group of low and high level change.

3. electrostatic precipitation high-frequency high-voltage source controller as claimed in claim 1, is characterized in that, the sliding-mode surface parameter of described fuzzy controller (3) to sliding mode controller (2) method regulated of adjusting is as follows:

It is given output voltage u that input language variable is selected in fuzzy control _refwith actual output voltage u _odifference e and output voltage deviation variation rate e _c, get sliding-mode surface parameter σ k _p, σ k _i, σ k _dwith σ k _cfor output language variable, according to overgauge and the minus deviation of output voltage detected value and output voltage actual value, deviation e and deviation ratio e _csize be divided into { negative large, in negative, negative little, zero, just little, center, honest } 7 fuzzy subsets, be denoted as that { NB, NM, NS, ZO, PS, PM, PB}, by deviation e and deviation ratio e _cquantize in the region of (-3,3) respectively, simultaneously by the output σ k of fuzzy controller _p, σ k _i, σ k _dwith σ k _cfuzzy subset be divided into negative large, in negative, negative little, zero, just little, center, honest seven fuzzy subsets, be denoted as { NB, NM, NS, ZO, PS, PM, PB}, is quantized to (-0.25,0.25), (-0.06 respectively, 0.06), (-3,3), (-1,1); Input quantity e and e _cmembership function be Gaussian, the membership function of output is triangular form, and sliding-mode surface setting algorithm of parameters is as follows:

k _p＝k _p′+σk _p，k _i＝k _i′+σk _i，k _d＝k _d′+σk _d，k _c＝k _c′+σk _c

Wherein k _p', k _i', k _d', k _c' be the sliding-mode surface parameter before adjusting.

4. electrostatic precipitation high-frequency high-voltage source controller as claimed in claim 3, is characterized in that, the sliding-mode surface parameter of described fuzzy controller (3) to sliding mode controller (2) is adjusted and regulated fuzzy rule used to be:

If?e?is?A?and?e _c?is?B；

THEN?σk _p?is?C，σk _i?is?D，σk _d?is?E，σk _c?is?F。

5. electrostatic precipitation high-frequency high-voltage source controller as claimed in claim 1, it is characterized in that, described fuzzy controller (3) is based on DSP.